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On nonlinear Riemann–Hilbert problems with discontinuous boundary condition

✍ Scribed by M. A. Efendiev; W. L. Wendland

Publisher
John Wiley and Sons
Year
2007
Tongue
English
Weight
199 KB
Volume
280
Category
Article
ISSN
0025-584X

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✦ Synopsis

Abstract

For holomorphic functions in the unit disc, we consider a general nonlinear boundary condition whose linearisation admits jump discontinuities at a finite number of points on the unit circle, the boundary of the unit disc. By using the properties of quasilinear Fredholm maps of the corresponding nonlinear Cauchy singular integral equation, the appropriate choice of the Gochberg–Krupnik index and a homotopy with linear Riemann–Hilbert problems with discontinuous coefficients, we show that the degree of mapping of the quasilinear Fredholm map is nonzero. This guaranties the existence of solutions. (© 2007 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)

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